Question: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 5$ $a_i = a_{i-1} - 6$ What is $a_{8}$, the eighth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $5$ and the common difference is $-6$ To find the eighth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 5 - 6(i - 1)$ To find $a_{8}$ , we can simply substitute $i = 8$ into the our formula. Therefore, the eighth term is equal to $a_{8} = 5 - 6 (8 - 1) = -37$.